Cave Story

Cave Story, or Doukutsu Monogatari, is a Japanese freeware
side-scrolling platform game.

Cave Story has leanings towards Wonderboy, recent
sidescrolling Castlevania titles, and is influenced by the Metroid
games. You control a little amnesiac who runs around helping out
Mimigas, a race of
sentient, bunny-like humanoids. You also try to find your way out
of the giant cave inside the floating island which makes up the game's
setting.

You can expand your health meter by collecting Life Capsules
in similar fashion to Metroid games, while you can get stronger by
collecting energy to boost your firearms output. Each weapon can be
built up to the maximum level (3) fairly quickly, but taking damage
will drain energy from its experience meter, sometimes causing it to
level down. Given how quickly they power up this only tends to be an
issue during boss fights, and even then there´s usually plenty of
opportunities for collecting more weapon energy.